fixed point arithmetic with respect to arbitrary bases and numbers of fraction digits,

infinite precision number in an arbitrary positional system as lazy lists of digits supporting also numbers with terminating representations,

polynomial, power series, Laurent series

root set of a polynomial,

matrix (basics only),

algebra, e.g., multi-variate polynomial (basics only),

permutation group.

Due to Haskell's flexible type system,
you can combine all these types,
e.g., fractions of polynomials, residue classes of polynomials,
complex numbers with physical units,
power series with real numbers as coefficients.

Using the revised system requires hiding some of the standard functions
provided by Prelude, which is fortunately supported by GHC.
The library has basic Cabal support
and a growing test-suite of QuickCheck tests
for the implemented mathematical objects.

Each data type now resides in a separate module.
Cyclic dependencies could be eliminated by fixing some types in class methods.
E.g., power exponents became simply Integer instead of Integral,
which has also the advantage of reduced type defaulting.

A still unsolved problem arises for
residue classes, matrix computations, infinite precision numbers,
fixed point numbers, and others.
It should be possible to assert statically
that the arguments of a function are residue classes with
respect to the same divisor, or that they are vectors of the same size.
Possible ways out are encoding values in types or local type
class instances. The latter one is still neither proposed nor
implemented in any Haskell compiler.
The modules are implemented in a way to keep all options open.
That is, for each number type there is one module
implementing the necessary operations
which expect the context as a parameter.
Then there are several modules
which provide different interfaces through type class instances
to these operations.